Homework Help:
Moment of Inertia of a Pyramid

1. The problem statement, all variables and given/known data
Ok not really a school problem but i was just thinking of how to solve it.

How would i find the moment of inertia of a pyramid with base side length l and height h?
If the axis of rotation is along the z axis?

2. Relevant equations

I = Summation of mrsquared

3. The attempt at a solution

Ok so my approach is to find the geometrical center of the pyramid first.

I would know its easy to cut each of the diagonal lengths by 2 and drawing a straight perpendicular line down, but i wanted to try some integration because i just learned it a week ago.
I had problems setting up the integral, so could anyone give me a hint or 2?